Turbine nozzle airfoil profile

ABSTRACT

A turbine nozzle for a turbine includes: an airfoil having a shape with a nominal profile substantially in accordance with at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I. The Cartesian coordinate values are non-dimensional values of from 0% to 100% convertible to distances by multiplying the values by a height of the airfoil expressed in units of distance. The X and Y values are connected by smooth continuing arcs to define airfoil profile sections at each distance Z along at least a portion of the airfoil, and the profile sections at the Z distances are joined smoothly with one another to form the nominal profile.

TECHNICAL FIELD

The subject matter disclosed herein relates to turbomachines. More particularly, the subject matter disclosed herein relates to a turbine nozzle airfoil profile for a turbine nozzle.

BACKGROUND

Some jet aircraft and simple or combined cycle power plant systems employ turbines, or so-called turbomachines, in their design and operation. Some of these turbines employ airfoils (e.g., turbine nozzles, blades, airfoils, etc.), which during operation are exposed to fluid flows. These airfoils are configured to aerodynamically interact with the fluid flows to generate energy from these fluid flows as part of power generation. For example, the airfoils may be used to create thrust, to convert kinetic energy to mechanical energy, and/or to convert thermal energy to mechanical energy. As a result of this interaction and conversion, the aerodynamic characteristics of these airfoils may result in losses in system and turbine operation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION OF THE DISCLOSURE

Various embodiments of the disclosure include turbine nozzles and systems employing such nozzles. Various particular embodiments include a turbine nozzle having: an airfoil having: a suction side; a pressure side opposing the suction side; a leading edge spanning between the pressure side and the suction side; and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, the pressure side, the trailing edge and the leading edge.

A first aspect of the disclosure includes a turbine nozzle comprising: an airfoil having: a suction side, a pressure side opposing the suction side, a leading edge spanning between the pressure side and the suction side, and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, the pressure side, the trailing edge and the leading edge, wherein at least one of a suction side or a pressure side of the airfoil has a shape having a nominal profile substantially in accordance with at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the Cartesian coordinate values are non-dimensional values of from 0% to 100% convertible to distances by multiplying the values by a height of the airfoil expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along at least a portion of the airfoil, the airfoil profile sections at the Z distances being joined smoothly with one another to form the nominal profile.

A second aspect of the disclosure includes a static nozzle section for a turbine, the static nozzle section comprising: a set of static nozzles, the set of static nozzles including at least one nozzle having: an airfoil having: a suction side, a pressure side opposing the suction side, a leading edge spanning between the pressure side and the suction side, and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, the pressure side, the trailing edge and the leading edge, wherein at least one of a suction side or a pressure side of the airfoil has a shape having a nominal profile substantially in accordance with at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the Cartesian coordinate values are non-dimensional values of from 0% to 100% convertible to distances by multiplying the values by a height of the airfoil expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along at least a portion of the airfoil, the airfoil profile sections at the Z distances being joined smoothly with one another to form the nominal profile.

A third aspect of the disclosure includes a turbine comprising a plurality of turbine nozzles, each of the turbine nozzles comprising: an airfoil having: a suction side, a pressure side opposing the suction side, a leading edge spanning between the pressure side and the suction side, and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, the pressure side, the trailing edge and the leading edge, wherein at least one of a suction side or a pressure side of the airfoil has a shape having a nominal profile substantially in accordance with at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the Cartesian coordinate values are non-dimensional values of from 0% to 100% convertible to distances by multiplying the values by a height of the airfoil expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along at least a portion of the airfoil, the airfoil profile sections at the Z distances being joined smoothly with one another to form the nominal profile.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features of this disclosure will be more readily understood from the following detailed description of the various aspects of the disclosure taken in conjunction with the accompanying drawings that depict various embodiments of the disclosure, in which:

FIG. 1 is a schematic illustration of an example turbomachine;

FIG. 2 is a cross-section illustration of an example gas turbine assembly with a four-stage turbine that may be used with the turbomachine in FIG. 1;

FIG. 3 shows a schematic three-dimensional view of an illustrative turbine nozzle including an airfoil and endwalls, according to various embodiments of the disclosure;

FIG. 4 shows a schematic three-dimensional view of a plurality of turbine nozzles, according to various embodiments of the disclosure;

FIG. 5 shows a schematic view of an origin of an airfoil of a turbine nozzle, according to various embodiments of the disclosure; and

FIG. 6 shows a schematic three-dimensional view of an illustrative turbine nozzle including an airfoil and endwalls, according to various embodiments of the disclosure.

It is noted that the drawings of the disclosure are not necessarily to scale. The drawings are intended to depict only typical aspects of the disclosure and therefore should not be considered as limiting the scope of the disclosure. In the drawings, like numbering represents like elements between the drawings.

DETAILED DESCRIPTION

As an initial matter, in order to clearly describe the current technology it will become necessary to select certain terminology when referring to and describing relevant machine components within a turbomachine. To the extent possible, common industry terminology will be used and employed in a manner consistent with its accepted meaning. Unless otherwise stated, such terminology should be given a broad interpretation consistent with the context of the present application and the scope of the appended claims. Those of ordinary skill in the art will appreciate that often a particular component may be referred to using several different or overlapping terms. What may be described herein as being a single part may include and be referenced in another context as consisting of multiple components. Alternatively, what may be described herein as including multiple components may be referred to elsewhere as a single part.

In addition, several descriptive terms may be used regularly herein, and it should prove helpful to define these terms at the onset of this section. These terms and their definitions, unless stated otherwise, are as follows. As used herein, “downstream” and “upstream” are terms that indicate a direction relative to the flow of a fluid, such as the working fluid through the turbine engine or, for example, the flow of air through the combustor or coolant through one of the turbine's component systems. The term “downstream” corresponds to the direction of flow of the fluid, and the term “upstream” refers to the direction opposite to the flow. The terms “forward” and “aft,” without any further specificity, refer to directions, with “forward” referring to the front or compressor end of the engine, and “aft” referring to the rearward or turbine end of the engine.

It is often required to describe parts that are disposed at differing radial positions with regard to a center axis. The term “radial” refers to movement or position perpendicular to an axis. For example, if a first component resides closer to the axis than a second component, it will be stated herein that the first component is “radially inward” or “inboard” of the second component. If, on the other hand, the first component resides further from the axis than the second component, it may be stated herein that the first component is “radially outward” or “outboard” of the second component. The term “axial” refers to movement or position parallel to an axis. Finally, the term “circumferential” refers to movement or position around an axis. It will be appreciated that such terms may be applied in relation to the center axis of the turbine.

In addition, several descriptive terms may be used regularly herein, as described below. The terms “first”, “second”, and “third” may be used interchangeably to distinguish one component from another and are not intended to signify location or importance of the individual components.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. “Optional” or “optionally” means that the subsequently described event or circumstance may or may not occur and that the description includes instances where the event occurs and instances where it does not.

Where an element or layer is referred to as being “on,” “engaged to,” “connected to” or “coupled to” another element or layer, it may be directly on, engaged to, connected to, or coupled to the other element or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being “directly on,” “directly engaged to,” “directly connected to” or “directly coupled to” another element or layer, there may be no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., “between” versus “directly between,” “adjacent” versus “directly adjacent,” etc.). As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items.

As noted herein, various aspects of the disclosure are directed toward turbine nozzles. Various embodiments include a turbine nozzle having: an airfoil having an airfoil shape having a nominal profile substantially in accordance with at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I. The Cartesian coordinate values are non-dimensional values of from 0% to 100% convertible to distances by multiplying the values by a height of the airfoil expressed in units of distance. The X and Y values are connected by smooth continuing arcs that define airfoil profile sections at each distance Z along at least a portion of the airfoil, and the profile sections at the Z distances are joined smoothly with one another to form the nominal airfoil profile.

Referring to the drawings, FIG. 1 is a schematic view of an illustrative turbomachine 90 in the form of a combustion turbine or gas turbine (GT) system 100 (hereinafter, “GT system 100”). GT system 100 includes a compressor 102 and a combustor 104. Combustor 104 includes a combustion region 105 and a fuel nozzle assembly 106. GT system 100 also includes a turbine 108 and a common compressor/turbine shaft 110 (hereinafter referred to as “rotor 110”). In one embodiment, GT system 100 is a 7HA.03 engine, commercially available from General Electric Company, Greenville, S.C. The present disclosure is not limited to any one particular GT system and may be implanted in connection with other engines including, for example, the other HA, F, B, LM, GT, TM and E-class engine models of General Electric Company and engine models of other companies. Further, the teachings of the disclosure are not necessarily applicable to only a GT system and may be applied to other types of turbomachines, e.g., steam turbines, jet engines, compressors, etc.

FIG. 2 shows a cross-section view of an illustrative portion of turbine 108 with four stages L0-L3 that may be used with GT system 100 in FIG. 1. The four stages are referred to as L0, L1, L2, and L3. Stage L0 is the first stage and is the smallest (in a radial direction) of the four stages. Stage L1 is the second stage and is the next stage in an axial direction. Stage L2 is the third stage and is the next stage in an axial direction. Stage L3 is the fourth, last stage and is the largest (in a radial direction). It is to be understood that four stages are shown as one example only, and each turbine may have more or less than four stages.

A set of stationary vanes or nozzles 112 cooperate with a set of rotating blades 114 to form each stage L0-L3 of turbine 108 and to define a portion of a flow path through turbine 108. Rotating blades 114 in each set are coupled to a respective rotor wheel 116 that couples them circumferentially to rotor 110. That is, a plurality of rotating blades 114 are mechanically coupled in a circumferentially spaced manner to each rotor wheel 116. A static nozzle section 115 includes a plurality of stationary nozzles 112 circumferentially spaced around rotor 110. Each nozzle 112 may include at least one endwall (or platform) 120, 122 connected with airfoil 130. In the example shown, nozzle 112 includes a radially outer endwall 120 and a radially inner endwall 122. Radially outer endwall 120 couples nozzle(s) 112 to a casing 124 of turbine 108.

In operation, air flows through compressor 102, and compressed air is supplied to combustor 104. Specifically, the compressed air is supplied to fuel nozzle assembly 106 that is integral to combustor 104. Fuel nozzle assembly 106 is in flow communication with combustion region 105. Fuel nozzle assembly 106 is also in flow communication with a fuel source (not shown in FIG. 1) and channels fuel and air to combustion region 105. Combustor 104 ignites and combusts fuel. Combustor 104 is in flow communication with turbine 108 within which gas stream thermal energy is converted to mechanical rotational energy. Turbine 108 is rotatably coupled to and drives rotor 110. Compressor 102 also is rotatably coupled to rotor 110. In the illustrative embodiment, there is a plurality of combustors 104 and fuel nozzle assemblies 106. In the following discussion, unless otherwise indicated, only one of each component will be discussed. At least one end of rotor 110 may extend axially away from turbine 108 and may be attached to a load or machinery (not shown), such as, but not limited to, a generator, a load compressor, and/or another turbine.

Turning to FIG. 3, a schematic three-dimensional view of a turbine nozzle (or simply, nozzle) 112 is shown, according to various embodiments to better illustrate the parts of a nozzle. Nozzle 112 is a stationary nozzle, which forms part of static nozzle section 115 (FIG. 2) and which forms part of an annulus of stationary nozzles in a stage of a turbine (e.g., turbine 108), as previously described. That is, during operation of a turbine (e.g., turbine 108), nozzle 112 will remain stationary in order to direct the flow of working fluid (e.g., gas or steam) to one or more movable blades (e.g., blades 114), causing those movable blades to initiate rotation of a rotor 110. It is understood that nozzle 112 may be configured to couple (mechanically couple via fasteners, welds, slot/grooves, etc.) with a plurality of similar or distinct nozzles (e.g., nozzles 112 or other nozzles) to form an annulus of nozzles in a stage L0-L3 of turbine 108.

Turbine nozzle 112 can include an airfoil 130 having a convex suction side 132, and a concave pressure side 134 (obstructed in FIG. 3) opposing suction side 132. Nozzle 112 can also include a leading edge 136 spanning between pressure side 134 and suction side 132 and a trailing edge 138 opposing leading edge 136 and spanning between pressure side 134 and suction side 132. As shown, and as previously noted, nozzle 112 can also include at least one endwall 120, 122 (two shown) connected with airfoil 130 along suction side 132, pressure side 134, trailing edge 138 and leading edge 136. In the example shown, nozzle 112 includes a radially outer endwall 120 and a radially inner endwall 122. Radially outer endwalls 120 are configured to align on the radially outer side of the static nozzle section and to couple respective nozzle(s) 112 to casing 124 (FIG. 2) of turbine 108 (FIG. 2). Radially inner endwalls 122 are configured to align on the radially inner side of static nozzle section 115 (FIG. 2). In various embodiments, nozzle 112 includes a fillet 140, 142 connecting airfoil 130 and each respective endwall 120, 122. Fillet 140 can include a weld or braze fillet, which may be formed via conventional metal-inert gas (MIG) welding, tungsten-inert gas (TIG) welding, brazing, etc. Fillets 140, 142 can overlap a portion of airfoil 130. The extent of overlap can vary from nozzle to nozzle, stage to stage, and/or turbine to turbine.

With reference again to FIG. 2, in various embodiments, nozzle 112 can include a first stage (L0) nozzle, second stage (L1) nozzle, third stage (L2) nozzle, or fourth stage (L3) nozzle. In particular embodiments, nozzle 112 is a second stage (L1) nozzle, and the improved flow profile across the interface between airfoil 130 and endwalls 120, 122 allows second stage (L1) nozzle to withstand high-temperature gas at the second stage. In various embodiments, turbine 108 can include a set of nozzles 112 in only first stage (L0) of turbine 108, or in only third stage (L2), or in only fourth stage (L3) of turbine 108.

With reference to FIG. 4 and with continuing reference to FIG. 3, suction side 132 and/or pressure side 134 of airfoil 130 shape has a nominal profile that can be expressed substantially in accordance with at least a portion of the Cartesian coordinates, i.e., X, Y, Z coordinates, set forth in TABLE I. A “profile” is the range of the variation between measured points on an airfoil surface and the ideal position listed in TABLE I. The actual profile on a manufactured turbine nozzle will be different from that defined by TABLE I, and the design is robust to this variation, meaning that mechanical and aerodynamic function are not impaired.

To allow for typical manufacturing tolerances and/or coating thicknesses, ±values can be added to the values listed in TABLE I, particularly to the X and Y values therein. For example, a tolerance of about 10-20 percent of a thickness of trailing edge 138 in a direction normal to any surface location along the airfoil profile can define an airfoil profile envelope for a nozzle airfoil design at cold or room temperature. In other words, a distance of about 10-20 percent of a thickness of the trailing edge in a direction normal to any surface location along the airfoil profile can define a range of variation between measured points on an actual airfoil surface and ideal positions of those points, particularly at a cold or room temperature, as embodied by the disclosure. The nozzle airfoil layout, as embodied by the disclosure, is robust to this range of variation without impairment of mechanical and aerodynamic functions.

The Cartesian coordinate system of X, Y and Z values given in TABLE I below defines the profile of the turbine nozzle airfoil (i.e., airfoil 130) at various locations along its height. To illustrate, FIG. 4 shows a plurality of cross sections 160-170 along span or height H that correspond to Z coordinate values of chord lines. Each cross section 160-170 of airfoil 130 can be described by a respective set of X and Y coordinates (from TABLE I). For example, 100 points can be listed for each of the pressure side and the suction side that define each cross section 160-170, though it should be apparent that more or fewer points can be used for the respective sides of each cross section, and more or fewer cross sections can be used, as may be desired and/or appropriate.

The coordinate values are stated as non-dimensional values of from 0% to 100% (percentages in TABLE I) convertible to distances by multiplying the values by a height H of airfoil 130 expressed in units of distance. While the X, Y, and Z coordinate values in TABLE I have been expressed in normalized or non-dimensionalized form, it should be apparent that any or all of the coordinate values could instead be expressed in distance units so long as the proportions are maintained. Specifically, the profile and/or layout can be scaled uniformly up or down, such as geometrically, without impairment of operation, and such scaling can be facilitated by use of normalized coordinate values, i.e., multiplying the normalized values by a common scaling factor, which may be a larger or smaller number of distance units than might have originally been used. For example, the values in TABLE I, particularly the X and Y values, could be multiplied by a scaling factor of 0.5, 2, or any other desired scaling factor, to uniformly geometrically scale. Alternatively, the values could be multiplied by a larger or smaller desired height H.

As discussed above, to convert an X, Y or Z value of TABLE I to a respective X, Y or Z coordinate value in units of distance, such as inches or meters, the non-dimensional X, Y or Z value given in TABLE I can be multiplied by a height H of airfoil 130 in such units of distance. Hence, the profile can be applied to airfoils of different heights H. By connecting the X and Y values with smooth continuing arcs, each profile cross section at each height Z (i.e., cross sections 160-170) can be fixed. The airfoil profiles of the various surface locations between the heights Z (in TABLE I) can be determined by smoothly connecting adjacent profile sections to one another, thus forming the nominal airfoil profile. Further, it is noted that where an airfoil profile section uses Z coordinate values not expressly stated in TABLE I, appropriate coordinate values can be mathematically extrapolated from TABLE I.

The values in TABLE I are generated and shown to three decimal places for determining the nominal profile of at least one of a suction side or a pressure side of airfoil 130 at ambient, non-operating, or non-hot conditions and do not take any coatings or fillets 140, 142 (FIG. 3) into account, though embodiments could account for other conditions, coatings, and/or fillets. The Cartesian coordinate values have an origin at an innermost point 172 (FIGS. 4 and 5) of leading edge 136 of airfoil 130 at the junction of airfoil 130 with a top surface of endwall 122. As shown in FIG. 5, it is understood that innermost point 172 may be covered by fillet 140 and that innermost point 172 is one of the points of cross section 160. Further, as shown in FIG. 4, cross sections 160 or 170 may be covered by fillet 140, 142, respectively.

While FIG. 4 shows nozzles 112 that employs all of the data from the Cartesian coordinate values of X, Y, and Z set forth in TABLE I (i.e., all data from 0% to 100%), it is possible that an airfoil profile for a nozzle uses only a selected portion or subset of Cartesian coordinate values of X, Y, and X set forth in TABLE I. For instance, while the Cartesian values in TABLE I provide Z coordinate values at 10% increments between 0% and 100%, only a portion of Cartesian coordinate values set forth in TABLE I may be employed. In one example, the airfoil profile sections may use a portion of Z coordinate values defined within 10% and 90% of the height of the airfoil, i.e., from cross sections 161 to 169. In another example, the airfoil profile sections may use a portion of the Cartesian coordinate values defined within 5% and 95% of the height of the airfoil, i.e., from a plane midway between cross sections 160 and 161 to a plane midway between cross sections 169 and 170. Any portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I may be employed, e.g., from 20% to 30%, 37%-50%, etc.

FIG. 6 shows a perspective view of a nozzle 112 that employs only a selected portion of the Cartesian coordinate values of X, Y and Z set forth in TABLE I to define a section of the span of the airfoil of nozzle 112. For example, a nozzle 112 may be made using coordinate values that represent a selected section of airfoil 130, such as from 40% of the height to 55% of the height, as shown by shading in FIG. 6. As shown in FIG. 6, a nozzle 112 that has, for example, a selected section of airfoil 130 may have an origin 172′ that dictates the relative position of the selected portion, e.g., 40%-55%, of the Cartesian coordinate values of X, Y and Z set forth in TABLE I. Coordinates other than those provided in TABLE I may be used to define the rest of the span of the airfoil of nozzle 112 (i.e., from 0% to 40% and from 55% to 100%), including the origin 172′ at a terminal end of the airfoil at its leading edge.

TABLE I Non-dimensionalized (%) N Location X Y Z 1 Suction-Side 0 0 0 2 Suction-Side −0.667 −1.106 0 3 Suction-Side −1.030 −2.347 0 4 Suction-Side −1.126 −3.639 0 5 Suction-Side −1.014 −4.929 0 6 Suction-Side −0.741 −6.197 0 7 Suction-Side −0.349 −7.431 0 8 Suction-Side 0.140 −8.632 0 9 Suction-Side 0.707 −9.798 0 10 Suction-Side 1.341 −10.928 0 11 Suction-Side 2.033 −12.024 0 12 Suction-Side 2.776 −13.086 0 13 Suction-Side 3.560 −14.118 0 14 Suction-Side 4.383 −15.120 0 15 Suction-Side 5.242 −16.091 0 16 Suction-Side 6.137 −17.029 0 17 Suction-Side 7.068 −17.931 0 18 Suction-Side 8.039 −18.789 0 19 Suction-Side 9.053 −19.596 0 20 Suction-Side 10.112 −20.343 0 21 Suction-Side 11.217 −21.020 0 22 Suction-Side 12.366 −21.623 0 23 Suction-Side 13.550 −22.148 0 24 Suction-Side 14.769 −22.590 0 25 Suction-Side 16.015 −22.944 0 26 Suction-Side 17.284 −23.207 0 27 Suction-Side 18.569 −23.377 0 28 Suction-Side 19.862 −23.457 0 29 Suction-Side 21.158 −23.446 0 30 Suction-Side 22.451 −23.347 0 31 Suction-Side 23.735 −23.164 0 32 Suction-Side 25.004 −22.904 0 33 Suction-Side 26.255 −22.570 0 34 Suction-Side 27.487 −22.166 0 35 Suction-Side 28.697 −21.699 0 36 Suction-Side 29.882 −21.174 0 37 Suction-Side 31.042 −20.596 0 38 Suction-Side 32.176 −19.969 0 39 Suction-Side 33.284 −19.296 0 40 Suction-Side 34.366 −18.582 0 41 Suction-Side 35.423 −17.830 0 42 Suction-Side 36.453 −17.045 0 43 Suction-Side 37.459 −16.226 0 44 Suction-Side 38.439 −15.379 0 45 Suction-Side 39.397 −14.506 0 46 Suction-Side 40.331 −13.607 0 47 Suction-Side 41.242 −12.684 0 48 Suction-Side 42.130 −11.740 0 49 Suction-Side 42.998 −10.777 0 50 Suction-Side 43.844 −9.795 0 51 Suction-Side 44.671 −8.798 0 52 Suction-Side 45.478 −7.782 0 53 Suction-Side 46.264 −6.753 0 54 Suction-Side 47.033 −5.708 0 55 Suction-Side 47.783 −4.651 0 56 Suction-Side 48.518 −3.583 0 57 Suction-Side 49.234 −2.503 0 58 Suction-Side 49.935 −1.413 0 59 Suction-Side 50.622 −0.313 0 60 Suction-Side 51.292 0.796 0 61 Suction-Side 51.951 1.913 0 62 Suction-Side 52.596 3.038 0 63 Suction-Side 53.228 4.169 0 64 Suction-Side 53.849 5.306 0 65 Suction-Side 54.460 6.451 0 66 Suction-Side 55.059 7.599 0 67 Suction-Side 55.650 8.754 0 68 Suction-Side 56.230 9.913 0 69 Suction-Side 56.801 11.077 0 70 Suction-Side 57.364 12.244 0 71 Suction-Side 57.918 13.416 0 72 Suction-Side 58.464 14.591 0 73 Suction-Side 59.004 15.769 0 74 Suction-Side 59.536 16.951 0 75 Suction-Side 60.062 18.136 0 76 Suction-Side 60.580 19.325 0 77 Suction-Side 61.092 20.515 0 78 Suction-Side 61.598 21.710 0 79 Suction-Side 62.098 22.905 0 80 Suction-Side 62.592 24.103 0 81 Suction-Side 63.081 25.304 0 82 Suction-Side 63.566 26.506 0 83 Suction-Side 64.044 27.711 0 84 Suction-Side 64.517 28.918 0 85 Suction-Side 64.987 30.127 0 86 Suction-Side 65.451 31.337 0 87 Suction-Side 65.911 32.548 0 88 Suction-Side 66.367 33.761 0 89 Suction-Side 66.819 34.977 0 90 Suction-Side 67.266 36.194 0 91 Suction-Side 67.709 37.411 0 92 Suction-Side 68.150 38.630 0 93 Suction-Side 68.587 39.851 0 94 Suction-Side 69.021 41.072 0 95 Suction-Side 69.453 42.294 0 96 Suction-Side 69.880 43.518 0 97 Suction-Side 69.932 43.885 0 98 Suction-Side 69.844 44.245 0 99 Suction-Side 69.630 44.548 0 100 Suction-Side 69.323 44.755 0 101 Pressure-Side 0 0 0 102 Pressure-Side 0.648 0.652 0 103 Pressure-Side 1.408 1.170 0 104 Pressure-Side 2.244 1.554 0 105 Pressure-Side 3.127 1.814 0 106 Pressure-Side 4.034 1.970 0 107 Pressure-Side 4.953 2.034 0 108 Pressure-Side 5.874 2.024 0 109 Pressure-Side 6.793 1.950 0 110 Pressure-Side 7.705 1.830 0 111 Pressure-Side 8.613 1.675 0 112 Pressure-Side 9.518 1.499 0 113 Pressure-Side 10.419 1.312 0 114 Pressure-Side 11.322 1.131 0 115 Pressure-Side 12.231 0.983 0 116 Pressure-Side 13.146 0.871 0 117 Pressure-Side 14.063 0.791 0 118 Pressure-Side 14.982 0.739 0 119 Pressure-Side 15.903 0.717 0 120 Pressure-Side 16.825 0.725 0 121 Pressure-Side 17.745 0.763 0 122 Pressure-Side 18.664 0.828 0 123 Pressure-Side 19.579 0.923 0 124 Pressure-Side 20.493 1.046 0 125 Pressure-Side 21.401 1.196 0 126 Pressure-Side 22.304 1.371 0 127 Pressure-Side 23.203 1.571 0 128 Pressure-Side 24.097 1.797 0 129 Pressure-Side 24.984 2.045 0 130 Pressure-Side 25.864 2.316 0 131 Pressure-Side 26.738 2.610 0 132 Pressure-Side 27.604 2.924 0 133 Pressure-Side 28.463 3.259 0 134 Pressure-Side 29.313 3.612 0 135 Pressure-Side 30.156 3.985 0 136 Pressure-Side 30.991 4.376 0 137 Pressure-Side 31.816 4.784 0 138 Pressure-Side 32.634 5.207 0 139 Pressure-Side 33.442 5.646 0 140 Pressure-Side 34.243 6.102 0 141 Pressure-Side 35.034 6.571 0 142 Pressure-Side 35.818 7.054 0 143 Pressure-Side 36.593 7.553 0 144 Pressure-Side 37.360 8.062 0 145 Pressure-Side 38.119 8.584 0 146 Pressure-Side 38.868 9.118 0 147 Pressure-Side 39.611 9.663 0 148 Pressure-Side 40.344 10.219 0 149 Pressure-Side 41.071 10.785 0 150 Pressure-Side 41.789 11.362 0 151 Pressure-Side 42.500 11.949 0 152 Pressure-Side 43.203 12.545 0 153 Pressure-Side 43.899 13.148 0 154 Pressure-Side 44.587 13.762 0 155 Pressure-Side 45.268 14.381 0 156 Pressure-Side 45.941 15.010 0 157 Pressure-Side 46.608 15.646 0 158 Pressure-Side 47.268 16.290 0 159 Pressure-Side 47.919 16.941 0 160 Pressure-Side 48.565 17.598 0 161 Pressure-Side 49.205 18.262 0 162 Pressure-Side 49.836 18.931 0 163 Pressure-Side 50.462 19.607 0 164 Pressure-Side 51.081 20.290 0 165 Pressure-Side 51.694 20.976 0 166 Pressure-Side 52.301 21.669 0 167 Pressure-Side 52.902 22.368 0 168 Pressure-Side 53.496 23.071 0 169 Pressure-Side 54.084 23.779 0 170 Pressure-Side 54.668 24.492 0 171 Pressure-Side 55.244 25.209 0 172 Pressure-Side 55.815 25.932 0 173 Pressure-Side 56.382 26.659 0 174 Pressure-Side 56.942 27.389 0 175 Pressure-Side 57.496 28.124 0 176 Pressure-Side 58.046 28.863 0 177 Pressure-Side 58.590 29.606 0 178 Pressure-Side 59.130 30.352 0 179 Pressure-Side 59.664 31.103 0 180 Pressure-Side 60.193 31.856 0 181 Pressure-Side 60.717 32.614 0 182 Pressure-Side 61.236 33.375 0 183 Pressure-Side 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Pressure-Side 64.349 39.174 10 191 Pressure-Side 64.817 39.953 10 192 Pressure-Side 65.281 40.734 10 193 Pressure-Side 65.741 41.517 10 194 Pressure-Side 66.195 42.304 10 195 Pressure-Side 66.645 43.093 10 196 Pressure-Side 67.088 43.887 10 197 Pressure-Side 67.331 44.177 10 198 Pressure-Side 67.664 44.357 10 199 Pressure-Side 68.039 44.406 10 200 Pressure-Side 68.407 44.317 10 1 Suction-Side −1.429 4.649 20 2 Suction-Side −2.149 3.549 20 3 Suction-Side −2.570 2.304 20 4 Suction-Side −2.732 0.997 20 5 Suction-Side −2.686 −0.318 20 6 Suction-Side −2.481 −1.620 20 7 Suction-Side −2.151 −2.896 20 8 Suction-Side −1.722 −4.142 20 9 Suction-Side −1.209 −5.357 20 10 Suction-Side −0.626 −6.539 20 11 Suction-Side 0.017 −7.688 20 12 Suction-Side 0.713 −8.807 20 13 Suction-Side 1.455 −9.897 20 14 Suction-Side 2.237 −10.958 20 15 Suction-Side 3.056 −11.990 20 16 Suction-Side 3.913 −12.993 20 17 Suction-Side 4.805 −13.963 20 18 Suction-Side 5.732 −14.900 20 19 Suction-Side 6.698 −15.796 20 20 Suction-Side 7.702 −16.650 20 21 Suction-Side 8.746 −17.454 20 22 Suction-Side 9.830 −18.202 20 23 Suction-Side 10.954 −18.891 20 24 Suction-Side 12.114 −19.515 20 25 Suction-Side 13.311 −20.069 20 26 Suction-Side 14.538 −20.550 20 27 Suction-Side 15.792 −20.954 20 28 Suction-Side 17.069 −21.275 20 29 Suction-Side 18.365 −21.515 20 30 Suction-Side 19.674 −21.668 20 31 Suction-Side 20.991 −21.735 20 32 Suction-Side 22.308 −21.716 20 33 Suction-Side 23.622 −21.615 20 34 Suction-Side 24.928 −21.433 20 35 Suction-Side 26.219 −21.173 20 36 Suction-Side 27.494 −20.840 20 37 Suction-Side 28.748 −20.437 20 38 Suction-Side 29.981 −19.968 20 39 Suction-Side 31.187 −19.439 20 40 Suction-Side 32.368 −18.852 20 41 Suction-Side 33.521 −18.212 20 42 Suction-Side 34.644 −17.526 20 43 Suction-Side 35.740 −16.792 20 44 Suction-Side 36.807 −16.019 20 45 Suction-Side 37.845 −15.207 20 46 Suction-Side 38.853 −14.359 20 47 Suction-Side 39.835 −13.478 20 48 Suction-Side 40.788 −12.567 20 49 Suction-Side 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44.651 20 197 Pressure-Side 66.868 44.945 20 198 Pressure-Side 67.197 45.130 20 199 Pressure-Side 67.572 45.182 20 200 Pressure-Side 67.939 45.093 20 1 Suction-Side −2.204 6.843 30 2 Suction-Side −2.925 5.725 30 3 Suction-Side −3.349 4.462 30 4 Suction-Side −3.511 3.136 30 5 Suction-Side −3.462 1.803 30 6 Suction-Side −3.251 0.485 30 7 Suction-Side −2.915 −0.808 30 8 Suction-Side −2.478 −2.069 30 9 Suction-Side −1.956 −3.298 30 10 Suction-Side −1.363 −4.495 30 11 Suction-Side −0.709 −5.660 30 12 Suction-Side −0.003 −6.793 30 13 Suction-Side 0.751 −7.896 30 14 Suction-Side 1.546 −8.969 30 15 Suction-Side 2.379 −10.012 30 16 Suction-Side 3.249 −11.026 30 17 Suction-Side 4.153 −12.009 30 18 Suction-Side 5.091 −12.960 30 19 Suction-Side 6.063 −13.876 30 20 Suction-Side 7.069 −14.754 30 21 Suction-Side 8.110 −15.590 30 22 Suction-Side 9.186 −16.380 30 23 Suction-Side 10.299 −17.118 30 24 Suction-Side 11.448 −17.798 30 25 Suction-Side 12.633 −18.417 30 26 Suction-Side 13.848 −18.968 30 27 Suction-Side 15.095 −19.448 30 28 Suction-Side 16.368 −19.851 30 29 Suction-Side 17.663 −20.175 30 30 Suction-Side 18.977 −20.412 30 31 Suction-Side 20.304 −20.562 30 32 Suction-Side 21.639 −20.625 30 33 Suction-Side 22.973 −20.598 30 34 Suction-Side 24.304 −20.485 30 35 Suction-Side 25.623 −20.286 30 36 Suction-Side 26.930 −20.006 30 37 Suction-Side 28.216 −19.648 30 38 Suction-Side 29.480 −19.217 30 39 Suction-Side 30.720 −18.717 30 40 Suction-Side 31.930 −18.155 30 41 Suction-Side 33.112 −17.532 30 42 Suction-Side 34.262 −16.855 30 43 Suction-Side 35.383 −16.129 30 44 Suction-Side 36.472 −15.356 30 45 Suction-Side 37.530 −14.542 30 46 Suction-Side 38.558 −13.688 30 47 Suction-Side 39.555 −12.800 30 48 Suction-Side 40.522 −11.878 30 49 Suction-Side 41.458 −10.926 30 50 Suction-Side 42.367 −9.946 30 51 Suction-Side 43.245 −8.941 30 52 Suction-Side 44.096 −7.912 30 53 Suction-Side 44.919 −6.861 30 54 Suction-Side 45.718 −5.789 30 55 Suction-Side 46.490 −4.699 30 56 Suction-Side 47.240 −3.595 30 57 Suction-Side 47.965 −2.474 30 58 Suction-Side 48.670 −1.340 30 59 Suction-Side 49.355 −0.192 30 60 Suction-Side 50.022 0.964 30 61 Suction-Side 50.671 2.132 30 62 Suction-Side 51.304 3.307 30 63 Suction-Side 51.923 4.491 30 64 Suction-Side 52.528 5.683 30 65 Suction-Side 53.120 6.879 30 66 Suction-Side 53.700 8.082 30 67 Suction-Side 54.270 9.291 30 68 Suction-Side 54.830 10.503 30 69 Suction-Side 55.380 11.719 30 70 Suction-Side 55.922 12.940 30 71 Suction-Side 56.457 14.164 30 72 Suction-Side 56.984 15.391 30 73 Suction-Side 57.505 16.621 30 74 Suction-Side 58.018 17.853 30 75 Suction-Side 58.527 19.089 30 76 Suction-Side 59.031 20.326 30 77 Suction-Side 59.528 21.565 30 78 Suction-Side 60.022 22.806 30 79 Suction-Side 60.511 24.049 30 80 Suction-Side 60.994 25.294 30 81 Suction-Side 61.475 26.540 30 82 Suction-Side 61.952 27.787 30 83 Suction-Side 62.425 29.036 30 84 Suction-Side 62.895 30.287 30 85 Suction-Side 63.363 31.537 30 86 Suction-Side 63.826 32.790 30 87 Suction-Side 64.287 34.043 30 88 Suction-Side 64.745 35.297 30 89 Suction-Side 65.202 36.553 30 90 Suction-Side 65.655 37.809 30 91 Suction-Side 66.107 39.066 30 92 Suction-Side 66.555 40.324 30 93 Suction-Side 67.002 41.582 30 94 Suction-Side 67.446 42.842 30 95 Suction-Side 67.890 44.102 30 96 Suction-Side 68.331 45.363 30 97 Suction-Side 68.385 45.742 30 98 Suction-Side 68.299 46.119 30 99 Suction-Side 68.086 46.441 30 100 Suction-Side 67.774 46.664 30 101 Pressure-Side −2.204 6.843 30 102 Pressure-Side −1.542 7.479 30 103 Pressure-Side −0.773 7.984 30 104 Pressure-Side 0.067 8.357 30 105 Pressure-Side 0.951 8.609 30 106 Pressure-Side 1.859 8.758 30 107 Pressure-Side 2.778 8.816 30 108 Pressure-Side 3.698 8.800 30 109 Pressure-Side 4.615 8.723 30 110 Pressure-Side 5.526 8.593 30 111 Pressure-Side 6.429 8.418 30 112 Pressure-Side 7.322 8.194 30 113 Pressure-Side 8.201 7.924 30 114 Pressure-Side 9.071 7.627 30 115 Pressure-Side 9.942 7.328 30 116 Pressure-Side 10.820 7.050 30 117 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Pressure-Side 37.245 11.409 30 147 Pressure-Side 38.026 11.894 30 148 Pressure-Side 38.800 12.394 30 149 Pressure-Side 39.563 12.907 30 150 Pressure-Side 40.317 13.434 30 151 Pressure-Side 41.063 13.974 30 152 Pressure-Side 41.797 14.526 30 153 Pressure-Side 42.525 15.091 30 154 Pressure-Side 43.243 15.666 30 155 Pressure-Side 43.951 16.253 30 156 Pressure-Side 44.651 16.851 30 157 Pressure-Side 45.343 17.458 30 158 Pressure-Side 46.025 18.076 30 159 Pressure-Side 46.699 18.703 30 160 Pressure-Side 47.364 19.337 30 161 Pressure-Side 48.021 19.982 30 162 Pressure-Side 48.670 20.634 30 163 Pressure-Side 49.310 21.295 30 164 Pressure-Side 49.943 21.963 30 165 Pressure-Side 50.567 22.639 30 166 Pressure-Side 51.184 23.322 30 167 Pressure-Side 51.793 24.013 30 168 Pressure-Side 52.394 24.708 30 169 Pressure-Side 52.989 25.411 30 170 Pressure-Side 53.575 26.120 30 171 Pressure-Side 54.154 26.836 30 172 Pressure-Side 54.725 27.558 30 173 Pressure-Side 55.290 28.284 30 174 Pressure-Side 55.848 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Suction-Side 67.476 44.795 40 95 Suction-Side 67.914 46.077 40 96 Suction-Side 68.349 47.360 40 97 Suction-Side 68.401 47.743 40 98 Suction-Side 68.313 48.123 40 99 Suction-Side 68.098 48.447 40 100 Suction-Side 67.783 48.670 40 101 Pressure-Side −2.964 9.161 40 102 Pressure-Side −2.299 9.812 40 103 Pressure-Side −1.525 10.328 40 104 Pressure-Side −0.679 10.713 40 105 Pressure-Side 0.215 10.975 40 106 Pressure-Side 1.133 11.131 40 107 Pressure-Side 2.062 11.197 40 108 Pressure-Side 2.994 11.186 40 109 Pressure-Side 3.922 11.113 40 110 Pressure-Side 4.845 10.986 40 111 Pressure-Side 5.760 10.809 40 112 Pressure-Side 6.664 10.588 40 113 Pressure-Side 7.555 10.319 40 114 Pressure-Side 8.436 10.013 40 115 Pressure-Side 9.312 9.695 40 116 Pressure-Side 10.191 9.391 40 117 Pressure-Side 11.079 9.110 40 118 Pressure-Side 11.976 8.858 40 119 Pressure-Side 12.880 8.633 40 120 Pressure-Side 13.791 8.437 40 121 Pressure-Side 14.707 8.270 40 122 Pressure-Side 15.629 8.132 40 123 Pressure-Side 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Pressure-Side 59.627 36.068 40 182 Pressure-Side 60.130 36.852 40 183 Pressure-Side 60.627 37.639 40 184 Pressure-Side 61.117 38.431 40 185 Pressure-Side 61.601 39.227 40 186 Pressure-Side 62.078 40.028 40 187 Pressure-Side 62.549 40.832 40 188 Pressure-Side 63.013 41.639 40 189 Pressure-Side 63.472 42.451 40 190 Pressure-Side 63.924 43.264 40 191 Pressure-Side 64.370 44.082 40 192 Pressure-Side 64.811 44.903 40 193 Pressure-Side 65.245 45.727 40 194 Pressure-Side 65.672 46.554 40 195 Pressure-Side 66.094 47.385 40 196 Pressure-Side 66.511 48.217 40 197 Pressure-Side 66.736 48.513 40 198 Pressure-Side 67.055 48.702 40 199 Pressure-Side 67.421 48.756 40 200 Pressure-Side 67.783 48.670 40 1 Suction-Side −3.718 11.472 50 2 Suction-Side −4.439 10.307 50 3 Suction-Side −4.852 8.998 50 4 Suction-Side −5.000 7.633 50 5 Suction-Side −4.936 6.260 50 6 Suction-Side −4.709 4.904 50 7 Suction-Side −4.353 3.576 50 8 Suction-Side −3.894 2.280 50 9 Suction-Side −3.350 1.018 50 10 Suction-Side −2.734 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Pressure-Side −3.718 11.472 50 102 Pressure-Side −3.051 12.136 50 103 Pressure-Side −2.274 12.667 50 104 Pressure-Side −1.419 13.064 50 105 Pressure-Side −0.517 13.339 50 106 Pressure-Side 0.411 13.505 50 107 Pressure-Side 1.352 13.580 50 108 Pressure-Side 2.295 13.574 50 109 Pressure-Side 3.235 13.504 50 110 Pressure-Side 4.169 13.377 50 111 Pressure-Side 5.096 13.199 50 112 Pressure-Side 6.011 12.976 50 113 Pressure-Side 6.917 12.710 50 114 Pressure-Side 7.810 12.408 50 115 Pressure-Side 8.696 12.084 50 116 Pressure-Side 9.582 11.762 50 117 Pressure-Side 10.475 11.460 50 118 Pressure-Side 11.378 11.189 50 119 Pressure-Side 12.289 10.946 50 120 Pressure-Side 13.207 10.729 50 121 Pressure-Side 14.132 10.540 50 122 Pressure-Side 15.061 10.379 50 123 Pressure-Side 15.995 10.248 50 124 Pressure-Side 16.933 10.147 50 125 Pressure-Side 17.873 10.075 50 126 Pressure-Side 18.815 10.031 50 127 Pressure-Side 19.758 10.017 50 128 Pressure-Side 20.701 10.033 50 129 Pressure-Side 21.643 10.079 50 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Pressure-Side 62.673 42.960 50 188 Pressure-Side 63.138 43.780 50 189 Pressure-Side 63.598 44.603 50 190 Pressure-Side 64.051 45.431 50 191 Pressure-Side 64.497 46.262 50 192 Pressure-Side 64.938 47.095 50 193 Pressure-Side 65.372 47.933 50 194 Pressure-Side 65.801 48.773 50 195 Pressure-Side 66.223 49.616 50 196 Pressure-Side 66.638 50.463 50 197 Pressure-Side 66.859 50.754 50 198 Pressure-Side 67.171 50.942 50 199 Pressure-Side 67.532 50.996 50 200 Pressure-Side 67.887 50.910 50 1 Suction-Side −4.472 13.685 60 2 Suction-Side −5.194 12.496 60 3 Suction-Side −5.602 11.167 60 4 Suction-Side −5.744 9.782 60 5 Suction-Side −5.675 8.390 60 6 Suction-Side −5.439 7.016 60 7 Suction-Side −5.076 5.669 60 8 Suction-Side −4.607 4.357 60 9 Suction-Side −4.054 3.078 60 10 Suction-Side −3.426 1.833 60 11 Suction-Side −2.736 0.621 60 12 Suction-Side −1.990 −0.557 60 13 Suction-Side −1.194 −1.702 60 14 Suction-Side −0.355 −2.815 60 15 Suction-Side 0.525 −3.895 60 16 Suction-Side 1.443 −4.945 60 17 Suction-Side 2.394 −5.964 60 18 Suction-Side 3.377 −6.953 60 19 Suction-Side 4.391 −7.911 60 20 Suction-Side 5.434 −8.835 60 21 Suction-Side 6.507 −9.726 60 22 Suction-Side 7.610 −10.578 60 23 Suction-Side 8.743 −11.389 60 24 Suction-Side 9.909 −12.155 60 25 Suction-Side 11.106 −12.869 60 26 Suction-Side 12.334 −13.529 60 27 Suction-Side 13.593 −14.128 60 28 Suction-Side 14.881 −14.661 60 29 Suction-Side 16.197 −15.123 60 30 Suction-Side 17.535 −15.509 60 31 Suction-Side 18.896 −15.813 60 32 Suction-Side 20.272 −16.031 60 33 Suction-Side 21.661 −16.158 60 34 Suction-Side 23.055 −16.191 60 35 Suction-Side 24.448 −16.130 60 36 Suction-Side 25.833 −15.975 60 37 Suction-Side 27.204 −15.726 60 38 Suction-Side 28.557 −15.387 60 39 Suction-Side 29.885 −14.964 60 40 Suction-Side 31.183 −14.459 60 41 Suction-Side 32.451 −13.879 60 42 Suction-Side 33.685 −13.229 60 43 Suction-Side 34.882 −12.515 60 44 Suction-Side 36.044 −11.744 60 45 Suction-Side 37.168 −10.920 60 46 Suction-Side 38.256 −10.049 60 47 Suction-Side 39.309 −9.134 60 48 Suction-Side 40.325 −8.180 60 49 Suction-Side 41.309 −7.192 60 50 Suction-Side 42.258 −6.170 60 51 Suction-Side 43.175 −5.120 60 52 Suction-Side 44.062 −4.045 60 53 Suction-Side 44.919 −2.945 60 54 Suction-Side 45.747 −1.823 60 55 Suction-Side 46.549 −0.684 60 56 Suction-Side 47.325 0.474 60 57 Suction-Side 48.077 1.648 60 58 Suction-Side 48.808 2.836 60 59 Suction-Side 49.516 4.037 60 60 Suction-Side 50.205 5.248 60 61 Suction-Side 50.876 6.471 60 62 Suction-Side 51.530 7.702 60 63 Suction-Side 52.167 8.943 60 64 Suction-Side 52.790 10.190 60 65 Suction-Side 53.399 11.444 60 66 Suction-Side 53.995 12.705 60 67 Suction-Side 54.578 13.970 60 68 Suction-Side 55.152 15.242 60 69 Suction-Side 55.714 16.517 60 70 Suction-Side 56.267 17.797 60 71 Suction-Side 56.811 19.081 60 72 Suction-Side 57.345 20.368 60 73 Suction-Side 57.873 21.659 60 74 Suction-Side 58.392 22.953 60 75 Suction-Side 58.905 24.249 60 76 Suction-Side 59.411 25.549 60 77 Suction-Side 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Pressure-Side 0.628 15.875 60 108 Pressure-Side 1.582 15.879 60 109 Pressure-Side 2.533 15.813 60 110 Pressure-Side 3.477 15.688 60 111 Pressure-Side 4.415 15.511 60 112 Pressure-Side 5.343 15.292 60 113 Pressure-Side 6.261 15.035 60 114 Pressure-Side 7.167 14.735 60 115 Pressure-Side 8.062 14.408 60 116 Pressure-Side 8.957 14.078 60 117 Pressure-Side 9.860 13.770 60 118 Pressure-Side 10.771 13.492 60 119 Pressure-Side 11.692 13.243 60 120 Pressure-Side 12.619 13.019 60 121 Pressure-Side 13.552 12.820 60 122 Pressure-Side 14.490 12.650 60 123 Pressure-Side 15.433 12.509 60 124 Pressure-Side 16.380 12.395 60 125 Pressure-Side 17.329 12.312 60 126 Pressure-Side 18.282 12.257 60 127 Pressure-Side 19.234 12.232 60 128 Pressure-Side 20.188 12.235 60 129 Pressure-Side 21.142 12.267 60 130 Pressure-Side 22.093 12.327 60 131 Pressure-Side 23.043 12.415 60 132 Pressure-Side 23.988 12.533 60 133 Pressure-Side 24.932 12.677 60 134 Pressure-Side 25.869 12.849 60 135 Pressure-Side 26.802 13.047 60 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27.204 90 155 Pressure-Side 42.814 27.763 90 156 Pressure-Side 43.601 28.339 90 157 Pressure-Side 44.376 28.928 90 158 Pressure-Side 45.141 29.531 90 159 Pressure-Side 45.896 30.147 90 160 Pressure-Side 46.640 30.776 90 161 Pressure-Side 47.372 31.417 90 162 Pressure-Side 48.094 32.069 90 163 Pressure-Side 48.808 32.733 90 164 Pressure-Side 49.509 33.409 90 165 Pressure-Side 50.201 34.094 90 166 Pressure-Side 50.881 34.791 90 167 Pressure-Side 51.553 35.496 90 168 Pressure-Side 52.213 36.212 90 169 Pressure-Side 52.863 36.936 90 170 Pressure-Side 53.504 37.670 90 171 Pressure-Side 54.135 38.413 90 172 Pressure-Side 54.756 39.163 90 173 Pressure-Side 55.367 39.921 90 174 Pressure-Side 55.969 40.687 90 175 Pressure-Side 56.561 41.460 90 176 Pressure-Side 57.145 42.240 90 177 Pressure-Side 57.718 43.026 90 178 Pressure-Side 58.283 43.820 90 179 Pressure-Side 58.838 44.620 90 180 Pressure-Side 59.386 45.426 90 181 Pressure-Side 59.923 46.238 90 182 Pressure-Side 60.453 47.055 90 183 Pressure-Side 60.973 47.878 90 184 Pressure-Side 61.486 48.706 90 185 Pressure-Side 61.990 49.540 90 186 Pressure-Side 62.485 50.379 90 187 Pressure-Side 62.971 51.222 90 188 Pressure-Side 63.451 52.070 90 189 Pressure-Side 63.921 52.922 90 190 Pressure-Side 64.383 53.780 90 191 Pressure-Side 64.837 54.641 90 192 Pressure-Side 65.284 55.507 90 193 Pressure-Side 65.723 56.376 90 194 Pressure-Side 66.153 57.250 90 195 Pressure-Side 66.577 58.126 90 196 Pressure-Side 66.991 59.008 90 197 Pressure-Side 67.193 59.290 90 198 Pressure-Side 67.485 59.473 90 199 Pressure-Side 67.826 59.525 90 200 Pressure-Side 68.162 59.442 90 1 Suction-Side −7.638 22.943 100 2 Suction-Side −8.326 21.668 100 3 Suction-Side −8.709 20.266 100 4 Suction-Side −8.831 18.814 100 5 Suction-Side −8.746 17.362 100 6 Suction-Side −8.496 15.930 100 7 Suction-Side −8.115 14.524 100 8 Suction-Side −7.626 13.151 100 9 Suction-Side −7.049 11.813 100 10 Suction-Side −6.397 10.509 100 11 Suction-Side −5.679 9.242 100 12 Suction-Side −4.902 8.012 100 13 Suction-Side −4.073 6.818 100 14 Suction-Side −3.195 5.657 100 15 Suction-Side −2.275 4.531 100 16 Suction-Side −1.313 3.438 100 17 Suction-Side −0.315 2.378 100 18 Suction-Side 0.717 1.349 100 19 Suction-Side 1.782 0.355 100 20 Suction-Side 2.877 −0.605 100 21 Suction-Side 4.003 −1.530 100 22 Suction-Side 5.159 −2.416 100 23 Suction-Side 6.344 −3.261 100 24 Suction-Side 7.559 −4.061 100 25 Suction-Side 8.804 −4.814 100 26 Suction-Side 10.080 −5.516 100 27 Suction-Side 11.384 −6.162 100 28 Suction-Side 12.714 −6.750 100 29 Suction-Side 14.071 −7.276 100 30 Suction-Side 15.453 −7.737 100 31 Suction-Side 16.857 −8.127 100 32 Suction-Side 18.278 −8.444 100 33 Suction-Side 19.714 −8.684 100 34 Suction-Side 21.162 −8.843 100 35 Suction-Side 22.615 −8.919 100 36 Suction-Side 24.070 −8.909 100 37 Suction-Side 25.522 −8.811 100 38 Suction-Side 26.965 −8.625 100 39 Suction-Side 28.394 −8.351 100 40 Suction-Side 29.805 −7.992 100 41 Suction-Side 31.191 −7.549 100 42 Suction-Side 32.550 −7.024 100 43 Suction-Side 33.876 −6.423 100 44 Suction-Side 35.167 −5.748 100 45 Suction-Side 36.419 −5.007 100 46 Suction-Side 37.632 −4.200 100 47 Suction-Side 38.803 −3.336 100 48 Suction-Side 39.931 −2.416 100 49 Suction-Side 41.017 −1.448 100 50 Suction-Side 42.061 −0.434 100 51 Suction-Side 43.064 0.621 100 52 Suction-Side 44.027 1.713 100 53 Suction-Side 44.951 2.837 100 54 Suction-Side 45.840 3.991 100 55 Suction-Side 46.692 5.172 100 56 Suction-Side 47.511 6.377 100 57 Suction-Side 48.299 7.601 100 58 Suction-Side 49.056 8.844 100 59 Suction-Side 49.787 10.104 100 60 Suction-Side 50.494 11.377 100 61 Suction-Side 51.175 12.663 100 62 Suction-Side 51.836 13.961 100 63 Suction-Side 52.477 15.267 100 64 Suction-Side 53.101 16.581 100 65 Suction-Side 53.709 17.905 100 66 Suction-Side 54.302 19.234 100 67 Suction-Side 54.883 20.569 100 68 Suction-Side 55.452 21.909 100 69 Suction-Side 56.010 23.254 100 70 Suction-Side 56.558 24.603 100 71 Suction-Side 57.098 25.955 100 72 Suction-Side 57.629 27.311 100 73 Suction-Side 58.152 28.669 100 74 Suction-Side 58.669 30.030 100 75 Suction-Side 59.178 31.396 100 76 Suction-Side 59.681 32.761 100 77 Suction-Side 60.178 34.130 100 78 Suction-Side 60.668 35.500 100 79 Suction-Side 61.155 36.872 100 80 Suction-Side 61.636 38.247 100 81 Suction-Side 62.111 39.623 100 82 Suction-Side 62.584 41.000 100 83 Suction-Side 63.052 42.379 100 84 Suction-Side 63.515 43.758 100 85 Suction-Side 63.975 45.140 100 86 Suction-Side 64.431 46.522 100 87 Suction-Side 64.886 47.905 100 88 Suction-Side 65.336 49.290 100 89 Suction-Side 65.785 50.675 100 90 Suction-Side 66.229 52.062 100 91 Suction-Side 66.673 53.448 100 92 Suction-Side 67.114 54.836 100 93 Suction-Side 67.552 56.224 100 94 Suction-Side 67.989 57.613 100 95 Suction-Side 68.423 59.003 100 96 Suction-Side 68.856 60.392 100 97 Suction-Side 68.901 60.781 100 98 Suction-Side 68.810 61.165 100 99 Suction-Side 68.598 61.498 100 100 Suction-Side 68.287 61.733 100 101 Pressure-Side −7.638 22.943 100 102 Pressure-Side −7.000 23.683 100 103 Pressure-Side −6.238 24.297 100 104 Pressure-Side −5.386 24.777 100 105 Pressure-Side −4.471 25.127 100 106 Pressure-Side −3.519 25.355 100 107 Pressure-Side −2.549 25.479 100 108 Pressure-Side −1.570 25.518 100 109 Pressure-Side −0.590 25.482 100 110 Pressure-Side 0.385 25.380 100 111 Pressure-Side 1.351 25.221 100 112 Pressure-Side 2.307 25.013 100 113 Pressure-Side 3.255 24.766 100 114 Pressure-Side 4.197 24.499 100 115 Pressure-Side 5.140 24.230 100 116 Pressure-Side 6.085 23.974 100 117 Pressure-Side 7.034 23.736 100 118 Pressure-Side 7.989 23.517 100 119 Pressure-Side 8.949 23.315 100 120 Pressure-Side 9.910 23.132 100 121 Pressure-Side 10.876 22.967 100 122 Pressure-Side 11.845 22.821 100 123 Pressure-Side 12.816 22.694 100 124 Pressure-Side 13.790 22.589 100 125 Pressure-Side 14.765 22.503 100 126 Pressure-Side 15.743 22.439 100 127 Pressure-Side 16.722 22.396 100 128 Pressure-Side 17.701 22.375 100 129 Pressure-Side 18.680 22.376 100 130 Pressure-Side 19.659 22.400 100 131 Pressure-Side 20.638 22.447 100 132 Pressure-Side 21.615 22.518 100 133 Pressure-Side 22.590 22.610 100 134 Pressure-Side 23.562 22.726 100 135 Pressure-Side 24.532 22.866 100 136 Pressure-Side 25.498 23.029 100 137 Pressure-Side 26.460 23.215 100 138 Pressure-Side 27.416 23.425 100 139 Pressure-Side 28.369 23.656 100 140 Pressure-Side 29.314 23.911 100 141 Pressure-Side 30.253 24.187 100 142 Pressure-Side 31.186 24.485 100 143 Pressure-Side 32.112 24.806 100 144 Pressure-Side 33.031 25.148 100 145 Pressure-Side 33.940 25.511 100 146 Pressure-Side 34.841 25.895 100 147 Pressure-Side 35.734 26.298 100 148 Pressure-Side 36.617 26.720 100 149 Pressure-Side 37.491 27.162 100 150 Pressure-Side 38.355 27.623 100 151 Pressure-Side 39.210 28.103 100 152 Pressure-Side 40.054 28.598 100 153 Pressure-Side 40.889 29.111 100 154 Pressure-Side 41.713 29.642 100 155 Pressure-Side 42.527 30.187 100 156 Pressure-Side 43.330 30.748 100 157 Pressure-Side 44.122 31.323 100 158 Pressure-Side 44.903 31.914 100 159 Pressure-Side 45.674 32.518 100 160 Pressure-Side 46.435 33.136 100 161 Pressure-Side 47.185 33.767 100 162 Pressure-Side 47.923 34.410 100 163 Pressure-Side 48.650 35.065 100 164 Pressure-Side 49.367 35.733 100 165 Pressure-Side 50.074 36.410 100 166 Pressure-Side 50.770 37.099 100 167 Pressure-Side 51.455 37.799 100 168 Pressure-Side 52.131 38.510 100 169 Pressure-Side 52.795 39.229 100 170 Pressure-Side 53.450 39.958 100 171 Pressure-Side 54.094 40.697 100 172 Pressure-Side 54.728 41.443 100 173 Pressure-Side 55.352 42.198 100 174 Pressure-Side 55.965 42.961 100 175 Pressure-Side 56.570 43.733 100 176 Pressure-Side 57.165 44.510 100 177 Pressure-Side 57.748 45.297 100 178 Pressure-Side 58.324 46.089 100 179 Pressure-Side 58.890 46.890 100 180 Pressure-Side 59.446 47.695 100 181 Pressure-Side 59.994 48.507 100 182 Pressure-Side 60.532 49.326 100 183 Pressure-Side 61.061 50.150 100 184 Pressure-Side 61.581 50.981 100 185 Pressure-Side 62.092 51.816 100 186 Pressure-Side 62.595 52.658 100 187 Pressure-Side 63.088 53.503 100 188 Pressure-Side 63.572 54.354 100 189 Pressure-Side 64.049 55.210 100 190 Pressure-Side 64.517 56.071 100 191 Pressure-Side 64.976 56.936 100 192 Pressure-Side 65.428 57.806 100 193 Pressure-Side 65.870 58.679 100 194 Pressure-Side 66.304 59.557 100 195 Pressure-Side 66.732 60.439 100 196 Pressure-Side 67.150 61.324 100 197 Pressure-Side 67.346 61.598 100 198 Pressure-Side 67.631 61.773 100 199 Pressure-Side 67.961 61.819 100 200 Pressure-Side 68.287 61.733 100

The disclosed airfoil shape provides a unique profile to achieve: 1) interaction between other stages in turbine 108 (FIG. 1); 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical nozzle or airfoil loadings. The disclosed loci of points defined in TABLE I allow GT system 100 or any other suitable turbine system to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil 130 may be adopted as long as: 1) interaction between other stages in the pressure turbine 108 (FIG. 1); 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical nozzle or airfoil loadings, are maintained in the scaled turbine.

Airfoil 130 described herein thus improves overall GT system 100 efficiency. Specifically, airfoil 130 provides a desired turbine efficiency lapse rate (ISO, hot, cold, part load, etc.). Airfoil 130 also meets all aeromechanical and stress requirements. Turbine nozzle 112 described herein has very specific aerodynamic design requirements. Significant cross-functional design effort was required to meet these design goals. Airfoil 130 of turbine nozzle 112 thus possesses a specific shape to meet aerodynamic, mechanical, and heat transfer requirements in an efficient and cost effective manner.

The apparatus and devices of the present disclosure are not limited to any one particular turbomachine, engine, turbine, jet engine, power generation system or other system, and may be used with turbomachines such as aircraft systems, power generation systems (e.g., simple cycle, combined cycle) and/or other systems (e.g., nuclear reactor). Additionally, the apparatus of the present disclosure may be used with other systems not described herein that may benefit from the increased efficiency of the apparatus and devices described herein.

Approximating language, as used herein throughout the specification and claims, may be applied to modify any quantitative representation that could permissibly vary without resulting in a change in the basic function to which it is related. Accordingly, a value modified by a term or terms, such as “about,” “approximately” and “substantially,” are not to be limited to the precise value specified. In at least some instances, the approximating language may correspond to the precision of an instrument for measuring the value. Here and throughout the specification and claims, range limitations may be combined and/or interchanged; such ranges are identified and include all the sub-ranges contained therein unless context or language indicates otherwise. “Approximately” as applied to a particular value of a range applies to both end values, and unless otherwise dependent on the precision of the instrument measuring the value, may indicate +/−10% of the stated value(s).

The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present disclosure has been presented for purposes of illustration and description but is not intended to be exhaustive or limited to the disclosure in the form disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the disclosure. The embodiment was chosen and described in order to best explain the principles of the disclosure and the practical application and to enable others of ordinary skill in the art to understand the disclosure for various embodiments with various modifications as are suited to the particular use contemplated. 

We claim:
 1. A turbine nozzle comprising: an airfoil having: a suction side, a pressure side opposing the suction side, a leading edge spanning between the pressure side and the suction side, and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, the pressure side, the trailing edge and the leading edge, wherein at least one of a suction side or a pressure side of the airfoil has a shape having a nominal profile in accordance with at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the Cartesian coordinate values are non-dimensional values of from 0% to 100% convertible to distances by multiplying the values by a height of the airfoil expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along at least a portion of the airfoil, the airfoil profile sections at the Z distances being joined smoothly with one another to form the nominal profile, wherein the shape having the nominal profile in accordance with the at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I includes the airfoil profile sections defined within 10% and 90% of the height of the airfoil.
 2. The turbine nozzle of claim 1, further comprising a fillet connecting a surface of the at least one endwall to a surface of the airfoil.
 3. The turbine nozzle of claim 1, wherein the at least one endwall includes an inner endwall or an outer endwall.
 4. The turbine nozzle of claim 1, wherein the turbine nozzle includes a second stage nozzle.
 5. The turbine nozzle of claim 1, wherein the shape having the nominal profile in accordance with the at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I includes the airfoil profile sections defined within 5% and 95% of the height of the airfoil.
 6. A static nozzle section for a turbine, the static nozzle section comprising: a set of static nozzles, the set of static nozzles including at least one nozzle having: an airfoil having: a suction side, a pressure side opposing the suction side, a leading edge spanning between the pressure side and the suction side, and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, the pressure side, the trailing edge and the leading edge, wherein at least one of a suction side or a pressure side of the airfoil has a shape having a nominal profile in accordance with at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the Cartesian coordinate values are non-dimensional values of from 0% to 100% convertible to distances by multiplying the values by a height of the airfoil expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along at least a portion of the airfoil, the airfoil profile sections at the Z distances being joined smoothly with one another to form the nominal profile, wherein the shape having the nominal profile in accordance with the at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I includes the airfoil profile sections defined within 10% and 90% of the height of the airfoil.
 7. The static nozzle section of claim 6, further comprising a fillet connecting a surface of the at least one endwall to a surface of the airfoil.
 8. The static nozzle section of claim 6, wherein the at least one endwall includes an inner endwall or an outer endwall.
 9. The static nozzle section of claim 6, wherein the static nozzle section is a second stage nozzle section.
 10. The static nozzle section of claim 6, wherein the shape having the nominal profile in accordance with at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I includes the airfoil profile sections defined within 5% and 95% of the height of the airfoil.
 11. A turbine comprising a plurality of turbine nozzles, each of the turbine nozzles comprising: an airfoil having: a suction side, a pressure side opposing the suction side, a leading edge spanning between the pressure side and the suction side, and a trailing edge opposing the leading edge and spanning between the pressure side and the suction side; and at least one endwall connected with the airfoil along the suction side, the pressure side, the trailing edge and the leading edge, wherein at least one of a suction side or a pressure side of the airfoil has a shape having a nominal profile in accordance with at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I, wherein the Cartesian coordinate values are non-dimensional values of from 0% to 100% convertible to distances by multiplying the values by a height of the airfoil expressed in units of distance, and wherein X and Y values connected by smooth continuing arcs define airfoil profile sections at each distance Z along at least a portion of the airfoil, the airfoil profile sections at the Z distances being joined smoothly with one another to form the nominal profile, wherein the shape having the nominal profile in accordance with the at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I includes the airfoil profile sections defined within 10% and 90% of the height of the airfoil.
 12. The turbine of claim 11, further comprising a fillet connecting a surface of the at least one endwall to a surface of the airfoil.
 13. The turbine of claim 11, wherein the at least one endwall includes an inner endwall or an outer endwall.
 14. The turbine of claim 11, wherein the turbine nozzle includes a second stage nozzle.
 15. The turbine of claim 11, wherein the shape having the nominal profile in accordance with the at least a portion of Cartesian coordinate values of X, Y and Z set forth in TABLE I includes the airfoil profile sections defined within 5% and 95% of the height of the airfoil. 